Observing the Ionization of Metastable States of Sn¹⁴⁺ in an Electron Beam Ion Trap

Abstract

This study investigates the ionization balance of Sn ions in an electron beam ion trap (EBIT). Highly charged Sn ions are produced via collisions with a quasi-monochromatic electron beam, and the charge state distribution is analyzed using a Wien filter. Significant Sn¹⁵⁺ production occurs at electron energies below the ionization potential of Sn¹⁴⁺ (379 eV). Calculations attribute this to electron-impact ionization from metastable Sn¹⁴⁺ states.

1. Introduction

Highly charged ions (HCIs) are of great interest in plasma physics and precision measurements in tests of fundamental physics [1,2,3,4,5,6]. In particular, ionization balance involving heavy ions is critical for understanding energy deposition in plasmas. Metastable states in HCIs, due to their long lifetime, tend to retain the electron population once excited. These long-lived states can significantly affect the charge state distribution (CSD), making them important for accurate plasma modeling [7,8].

An EBIT provides a controlled environment for probing such effects in detail. By generating and confining HCIs using a quasi-monochromatic electron beam, EBITs enable precise measurements of charge states and excitation dynamics. Combined with theoretical models, they are powerful tools for investigating metastable-related ionization processes [9,10,11,12].

In this work, we investigate the ionization equilibrium of highly charged tin ions in an EBIT with various electron-impact energies. We report the observation of electron excitation ionization in a low-density plasma.

2. Experiment

The experiments were performed using the low-energy permanent-magnet EBIT, CUBIT [13,14], as shown in Figure 1. Electrons are emitted from a LaB₆ cathode and accelerated by the potential difference between the cathode and the central drift tube (DT). The beam is simultaneously radially compressed by a 0.56 T magnetic field generated by a permanent magnet. Injected neutral atoms undergo successive electron-impact ionization to form highly charged ions. These ions are axially confined by an electrostatic potential well and radially by the combined effects of the magnetic field and the electron beam space charge. A charge-state diagnostic system, comprising a Wien filter and a microchannel plate (MCP) detector, enables direct CSD analysis within the trap.

Upon reaching ionization equilibrium within the EBIT, the ions were extracted by lowering the potential of DT3, and their abundances were measured using the CSD analyzer. Sn¹⁵⁺ ions were unexpectedly detected at an electron beam energy of 320 eV, well below the ionization potential of Sn¹⁴⁺ (379 eV) [15]. Figure 2a shows the CSDs at selected energies, each taken after a 1 s confinement time. Figure 2b presents the time evolution of ${\mathrm{Sn}}^{13+}$–${\mathrm{Sn}}^{15+}$ abundances at 350 eV, indicating that equilibrium is reached at 500 ms. A 1 s duration was thus used for subsequent measurements to ensure equilibrium. During the measurements, the electron beam current was kept at 5 mA, and the beam energy was scanned from 265 eV to 450 eV.

3. Theoretical Calculations

In this study, FAC (Flexible Atomic Code) [16] was employed to determine the energy levels, electron-impact excitation, radiative recombination cross-sections, and transition probabilities of Sn¹⁴⁺.

In the EBIT, the plasma has low electron density and a nearly monoenergetic electron energy distribution [17]. Under these conditions, the population of an energy level j is mainly governed by electron collisional excitation and de-excitation, along with spontaneous radiative decay. Processes such as dielectronic recombination, three-body recombination, charge exchange, and ion escape are negligible and thus omitted. The population rate equation for level i is given by

$${\displaystyle \frac{d{n}_i}{dt}}=\sum _{j>i}{n}_j{A}_{j\to i}+n_e\sum _{j<i}{n}_j{C}_{j\to i}^e+n_e\sum _{j>i}{n}_j{C}_{j\to i}^d$$

$$-\sum _{j<i}{n}_i{A}_{i\to j}-n_e\sum _{j>i}{n}_i{C}_{i\to j}^e-n_e\sum _{j<i}{n}_i{C}_{i\to j}^d.$$

(1)

Here, $A_{i\to j}$ is the spontaneous emission rate, while $C^e$ and $C^d$ denote the electron-impact excitation and de-excitation rates, respectively. At steady state, $d{n}_i/dt=0$, and together with the normalization ${\sum }_i{n}_i=1$, the level populations $n_i$ can be obtained.

In this study, the level structure and atomic processes of Sn¹⁴⁺ were analyzed. The main configurations used in the calculations are listed in

Table 1. The configurations included in the RCI-CRM calculations for Sn¹⁴⁺.

Ground Config.	$4{\mathit{s}}^{2}4{\mathit{p}}^6$
Single excitation	$4s^{2}4p^{5}4l(l=2,3)$
	$4s^{2}4p^{5}nl(n=5,6,l<n)$
	$4s4p^{6}4l(l=2,3)$
	$4s4p^{6}nl(n=5,6,l<n)$
Double excitations	$4s^{2}4p^{4}4l^2(l=2,3)$
	$4s^{2}4p^{4}4l5l^{\prime }(l=2,3,l^{\prime }\le 4)$
	$4s^{2}4p^{4}5l^2(l\le 4)$
	$4s4p^{5}4l^2(l=2,3)$
	$4s4p^{5}4l5l^{\prime }(l=2,3,l^{\prime }\le 4)$
	$4s4p^{5}5l^2(l\le 4)$
	$4p^{6}4l^2(l=2,3)$
	$4p^{6}4l5l^{\prime }(l=2,3,l^{\prime }\le 4)$
	$4p^{6}5l^2(l\le 4)$
Triple excitations	$4s^{2}4p^{3}4l^3(l=2,3)$
	$4s4p^{4}4l^3(l=2,3)$
	$4p^{5}4l^3(l=2,3)$

, with a total of 22,988 levels considered.

4. Results and Discussion

The results obtained at electron beam energies ranging from 265 eV to 450 eV are presented in Figure 3. As shown in the figure, ${\mathrm{Sn}}^{15+}$ ions begin to appear at an electron energy of 265 eV, which is significantly lower than the ionization potential of ${\mathrm{Sn}}^{14+}$ (379 eV). The relative abundance of ${\mathrm{Sn}}^{15+}$ ions reaches a maximum of approximately 50% at 355 eV and subsequently decreases with increasing electron energy. This behavior suggests that metastable ionization processes may have contributed to the transition from ${\mathrm{Sn}}^{14+}$ to ${\mathrm{Sn}}^{15+}$, and possibly also to the subsequent ionization from ${\mathrm{Sn}}^{15+}$ to ${\mathrm{Sn}}^{16+}$. Furthermore, there is a clear difference in the rate of increase of the ${\mathrm{Sn}}^{15+}$ abundance between the 265–320 eV and 320–355 eV energy intervals. We therefore hypothesize that multiple metastable ionization channels are involved, which will be examined in more detail in the following theoretical analysis section.

Figure 4 shows the distribution of the energy level of ${\mathrm{Sn}}^{14+}$ below the excitation energy of 200 eV. These levels, originating from the configurations listed in Table 1, include several metastable states with long lifetimes, particularly those associated with the $4p^{5}4d$ and $4p^{4}4d^2$ configurations. The relatively high excitation energies (ranging from 70 eV to 150 eV) and the extended lifetimes of these levels suggest that they can serve as initial states for ionization processes, especially in environments where the electron energy is insufficient to ionize the ground state directly. This interpretation is supported by experimental observations presented in Figure 3, where ${\mathrm{Sn}}^{15+}$ ions are detected at electron beam energies as low as 265 eV. The presence of these ions implies that metastable ionization pathways are active.

To investigate the ionization dynamics and level population behavior of ${\mathrm{Sn}}^{14+}$ in the EBIT environment, a steady-state collisional-radiative model (CRM) was employed. This model incorporates the dominant atomic processes under EBIT conditions, including electron collisional excitation and de-excitation, as well as spontaneous radiative decay. Electron-impact ionization and radiative recombination were not considered in the level population calculation. Transitions between all single and double excited configurations were considered, including electric dipole (E1), electric quadrupole (E2), magnetic dipole (M1), and magnetic quadrupole (M2) transitions.

The simulations were performed using the experimental parameters, including an electron beam current of 5 mA and an electron density of $1.1\times {10}^{-11}$ cm⁻³ [18,19]. The incident electron beam energies were corrected based on the calibration model described in the Section 2, yielding adjusted energies of 271, 322, 352, and 377 eV. The resulting populations of the highest-lying energy levels under these conditions are summarized in

Table 2. The 14 levels with the highest population for Sn¹⁴⁺ at different incident electron energies.

No.	E (eV)	Configuration	Lifetime(s)	27l eV	322 eV	352 eV	377 eV
1	0.0	${\left[4p^6\right]}_0$	∖	20.1%	14.0%	13.6%	20.0%
2	66.5	${\left[4p_{1/2}^{2}4p_{3/2}^{3}4d_{3/2}\right]}_0$	∞	0.8%	0.9%	1.0%	1.0%
3	69.8	${\left[4p_{1/2}^{2}4p_{3/2}^{3}4d_{5/2}\right]}_2$	$2.31\times {10}^{-3}$	7.8%	8.0%	8.2%	8.2%
4	70.1	${\left[4p_{1/2}^{2}4p_{3/2}^{3}4d_{3/2}\right]}_3$	$1.81\times {10}^1$	12.6%	12.9%	13.2%	12.9%
5	70.3	${\left[4p_{1/2}^{2}4p_{3/2}^{3}4d_{5/2}\right]}_4$	$1.59\times {10}^1$	25.0%	28.4%	29.2%	26.0%
6	71.5	${\left[4p_{1/2}^{2}4p_{3/2}^{3}4d_{3/2}\right]}_2$	$3.32\times {10}^{-2}$	6.8%	6.7%	6.7%	7.0%
7	74.1	${\left[4p_{1/2}^{2}4p_{3/2}^{3}4d_{5/2}\right]}_3$	$4.32\times {10}^{-2}$	10.5%	10.6%	10.6%	10.6%
8	79.0	${\left[4p_{1/2}4p_{3/2}^{4}4d_{3/2}\right]}_2$	$1.57\times {10}^{-4}$	2.9%	2.5%	2.2%	2.5%
9	81.1	${\left[4p_{1/2}4p_{3/2}^{4}4d_{5/2}\right]}_2$	$1.63\times {10}^{-4}$	2.6%	2.2%	1.9%	2.2%
10	82.2	${\left[4p_{1/2}4p_{3/2}^{4}4d_{5/2}\right]}_3$	$1.79\times {10}^{-4}$	3.6%	2.8%	2.4%	2.9%
11	139.5	${\left[4p_{1/2}^2{\left(4p_{3/2}^2\right)}_2{\left(4d_{5/2}^2\right)}_4\right]}_6$	$5.59\times {10}^{-3}$	2.6%	4.4%	4.6%	2.6%
12	144.9	${\left[4p_{1/2}^2{\left(4p_{3/2}^2\right)}_{2}4d_{3/2}4d_{5/2}\right]}_6$	$7.09\times {10}^{-3}$	2.3%	3.6%	3.8%	2.3%
13	151.8	${\left[4p_{1/2}4p_{3/2}^{3}4d_{3/2}4d_{5/2}\right]}_6$	$2.11\times {10}^{-4}$	0.9%	1.1%	1.0%	0.7%
14	155.0	${\left[4p_{1/2}{\left(4p_{3/2}^3\right)}_2{\left(4d_{5/2}^2\right)}_4\right]}_6$	$2.27\times {10}^{-4}$	0.6%	0.7%	0.7%	0.5%

. Their corresponding lifetimes are also listed in the same table for reference. The lifetime of the second level, ${\left[4p_{1/2}^{2}4p_{3/2}^{3}4d_{3/2}\right]}_0$, is effectively infinite in the present calculation, since single-photon decay is completely forbidden for this state and the two-photon transition is extremely weak. It is worth noting that the EBIT magnetic field may have an effect on its lifetime due to magnetic-field-induced transitions. Magnetic-field-induced mixing between the states $\left|{\left[4p_{1/2}^{2}4p_{3/2}^{3}4d_{3/2}\right]}_0,M\right.〉$ and $\left|{\left[4p_{1/2}^{2}4p_{3/2}^{4}4d_{3/2}\right]}_1,M\right.〉$ was estimated using the method introduced in [20], and the mixing coefficient $c\left(B\right)$ was found to be smaller than ${10}^{-5}$ at $B=0.56\mathrm{T}$. Since the transition amplitude induced by magnetic interactions can be expressed as $A_{\mathrm{MIT}}\propto {\left|c\left(B\right)\right|}^2·A({\left[4p_{1/2}^{2}4p_{3/2}^{4}4d_{3/2}\right]}_1\to \left[4p^6\right])$, with $A({\left[4p_{1/2}^{2}4p_{3/2}^{4}4d_{3/2}\right]}_1\to \left[4p^6\right])=7.6\times {10}^7{\mathrm{s}}^{-1}$, the estimated contribution is on the order of ${10}^{-3}{\mathrm{s}}^{-1}$. Therefore, the magnetic-field-induced transition can be neglected.

Table 2 reveals that the metastable configuration $4p^{5}4d$, particularly the $J=4$ level, consistently exhibits the highest population among all configurations at the four impact electron energies, reaching a peak of 29.2% at 352 eV. This metastable state may dominate in the intermediate stages of the ionization process of ${\mathrm{Sn}}^{14+}$. In contrast, the ground-state configuration $4p^6$ maintains a relatively stable population ranging from 13% to 20%, with its maximum population (20.0%) observed at 377 eV. The other $4p^{5}4d$ levels with lower total angular momentum quantum numbers ($J=3,2$) also show substantial populations, typically ranging between 6% and 13%. These levels, with longer lifetimes and lower radiative decay rates, serve as metastable states that significantly contribute to multi-step ionization dynamics. Highly excited configurations such as $4p^{4}4d^2$ and $4p^{4}4d4f$ begin to emerge. However, their populations remain consistently below 3%, reflecting their limited stability and transient existence before undergoing further ionization.

Overall, the population distributions in Table 2 may suggest the involvement of two possible ionization pathways for ${\mathrm{Sn}}^{14+}$. One is likely associated with metastable $4p^{5}4d$ states, which dominate the population and could serve as favorable precursors for ionization. The other may involve direct excitation to higher configurations such as $4p^{4}4d^2$ and $4p^{4}4d4f$, which, although weakly populated, appear at higher excitation energies and might contribute to ionization toward ${\mathrm{Sn}}^{15+}$ at low incident electron energies.

5. Conclusions

We studied the ionization dynamics of Sn¹⁴⁺ ions in an EBIT under controlled electron energies. Sn¹⁵⁺ ions were produced even below the ionization potential of Sn¹⁴⁺, which is attributed to ionization from metastable states. We observed double-electron excitation ionization in a low-density plasma. Experimental and theoretical results confirm multiple ionization pathways and reveal the complexity of EBIT ionization processes.